Question

A computer has a list of n possible passwords. If only one is accepted, what is the probability of guessing the password right on the first try?

Answer 1

1 / n

Answer 2

thank you. that makes sense. 1/total. However, I am now trying to find the P(correct on 3rd try). Is that P(wrong) * P(wrong) * P(right). if so is that (n-1)/n * (n-1)/(n-1) * 1/(n-2)?

Answer 3

on the second term i mean n-2/n-1

Answer 4

Assuming we can't repeat passwords, that looks correct.

Answer 5

ok, so extrapolating to (if i <n, on the ith try). I think that it should be something like ((n-1)^(i-1) * 1)/ (n*(n-1)...(n-i)). I can't remember what the formula for the sum of products is though.

Answer 6

actually on the last term of the denominator i think it would be n-(i-1)

Answer 7

I've got to go now, but you certainly could extrapolate like that. To write it exactly, you could do a lot of canceling, or you could write it in product notation using this symbol. \[\prod\]

Answer 8

thank you very much KingGeorge.